Accurate basket catheter tracking

ABSTRACT

In one embodiment, a system includes a catheter including an insertion tube and a first position sensor, a pusher including a second position sensor, and an expandable assembly including flexible strips disposed circumferentially around a distal portion of the pusher, with first ends of the strips connected to the distal end of the insertion tube and second ends of the strips connected to the distal portion of the pusher, the flexible strips bowing radially outward when the pusher is retracted, processing circuitry to receive a respective position signal from the first and second position sensors, compute location and orientation coordinates for the position sensors subject to a constraint that the position sensors are coaxial and have a same orientation, compute a distance between the computed location coordinates of the position sensors, and find position coordinates of the flexible strips responsively to at least the computed distance.

RELATED APPLICATION INFORMATION

This application is a divisional of prior filed U.S. patent applicationSer. No. 16/854,538 filed on Apr. 21, 2020, which claims benefit of U.S.Provisional Patent Application No. 62/892,487 of Beeckler, et al. filedon Aug. 27, 2019, which prior application is hereby incorporated byreference as if set forth in full into this application.

FIELD OF THE INVENTION

The present invention relates to medical devices, and in particular to,tracking position of catheters.

BACKGROUND

A wide range of medical procedures involve placing probes, such ascatheters, within a patient's body. Location sensing systems have beendeveloped for tracking such probes. Magnetic location sensing is one ofthe methods known in the art. In magnetic location sensing, magneticfield generators are typically placed at known locations external to thepatient. A magnetic field sensor within the distal end of the probegenerates electrical signals in response to these magnetic fields, whichare processed to determine the coordinate locations of the distal end ofthe probe. These methods and systems are described in U.S. Pat. Nos.5,391,199, 6,625,563, 6,690,963, 6,484,118, 6,239,724, 6,618,612 and6,332,089, in PCT International Publication No. WO 1996/005768, and inU.S. Patent Application Publications Nos. 2003/0120150 and 2004/0068178,whose disclosures are all incorporated herein by reference. Locationsmay also be tracked using impedance or current based systems.

European Patent Publication 3,178,384 of Hoitink, et al., describes acatheter having a dual node multiray electrode assembly at the distalend of the catheter body. The dual node multiray electrode assemblyincludes a proximal multiray array with a plurality of spines connectedat one end, each spine having at least one ablation electrode, and adistal node. The dual node multiray electrode assembly may have anexpanded configuration and a collapsed configuration wherein the spinesare arranged generally along a longitudinal axis of the catheter body.The distal node may be configured to be deployed within a vessel and theproximal multiray array may be configured to engage tissue forming anostium of the vessel with the ablation electrodes. In some embodiments,the relative distance between the proximal multiray array and the distalnode is adjustable.

US Patent Publication 2017/0181706 of Montag, et al., describescatheterization of the heart being carried out using a framework formedby a plurality of electrically conducting wire loops. The wire loops aremodeled as polygons, each subdivided into a plurality of triangles. Thewire loops are exposed to magnetic fluxes at respective frequencies, andsignals read from the loops. Theoretical magnetic fluxes in the polygonsare computed as sums of theoretical magnetic fluxes in the trianglesthereof. The location and orientation of the framework in the heart isdetermined by relating the computed theoretical magnetic fluxes to thesignals.

US Patent Publication 2015/0025365 of Esguerra, et al., describes acatheter having single axis sensors mounted directly along a portion ofthe catheter whose position/location is of interest. The magnetic based,single axis sensors are on a linear or nonlinear single axis sensor(SAS) assembly. The catheter includes a catheter body and a distal 2D or3D configuration provided by a support member on which at least one, ifnot at least three single axis sensors, are mounted serially along alength of the support member. The magnetic-based sensor assembly mayinclude at least one coil member wrapped on the support member, whereinthe coil member is connected via a joint region to a respective cablemember adapted to transmit a signal providing location information fromthe coil member to a mapping and localization system. The joint regionprovides strain relief adaptations to the at least one coil member andthe respective cable member from detaching.

US Patent Publication 2015/0150472 of Harley, et al., describes anon-contact cardiac mapping method that includes: (i) inserting acatheter into a heart cavity having an endocardium surface, the catheterincluding multiple, spatially distributed electrodes; (ii) measuringsignals at the catheter electrodes in response to electrical activity inthe heart cavity with the catheter spaced from the endocardium surface;and (iii) determining physiological information at multiple locations ofthe endocardium surface based on the measured signals and positions ofthe electrodes with respect to the endocardium surface.

US Patent Publication 2006/0009689 of Fuimaono, et al., describes animproved basket catheter is provided that is particularly useful formapping the heart. The catheter comprises an elongated catheter bodyhaving proximal and distal ends and at least one lumen therethrough. Abasket-shaped electrode assembly is mounted at the distal end of thecatheter body. The basket assembly has proximal and distal ends andcomprises a plurality of spines connected at their proximal and distalends. Each spine comprises at least one electrode. The basket assemblyhas an expanded arrangement wherein the spines bow radially outwardlyand a collapsed arrangement wherein the spines are arranged generallyalong the axis of the catheter body. The catheter further comprises adistal location sensor mounted at or near the distal end of thebasket-shaped electrode assembly and a proximal location sensor mountedat or near the proximal end of the basket-shaped electrode assembly. Inuse, the coordinates of the distal location sensor relative to those ofthe proximal sensor can be determined and taken together with knowninformation pertaining to the curvature of the spines of thebasket-shaped mapping assembly to find the positions of the at least oneelectrode of each spine.

US Patent Publication 2002/0198676 of Kirsch, et al., describes a systemfor determining the position, orientation and system gain factor of aprobe includes a plurality of magnetic field sources and at least onemagnetic field sensor, such that a combination of a magnetic fieldsensor and a magnetic field source generates a unique measured magneticfield value. The system includes a probe whose gain, position, andorientation affect these unique measured magnetic field values. Aprocessor is configured to receive and iteratively process these uniquemeasured magnetic field values to determine a system gain factorindicative of the gain of the probe and a plurality of location factorsindicative of the position and orientation of the probe. The number ofunique measured magnetic field values generated must be at least equalto the sum of the number of gain and location factors calculated.

The background section of Kirsch, et al., mentions that determining aprobe's location and orientation from magnetic field measurements is notstraight forward because the measured magnetic fields are nonlinearfunctions of the location and orientation. To determine the probe'slocation and orientation from the measured magnetic field values, theprobes location and orientation are first presumed or “guessed” to be ata predicted location and orientation. An iterative process is used tocompare values of the magnetic field at the guessed probe location andorientation with the measured field values. If the magnetic field valuesat a guessed location and orientation are close to the measured values,the guessed location and orientation are presumed to accuratelyrepresent the actual location and orientation of the probe. Theiterative process uses a physical model for the probe's environment. Thephysical model specifies the location and orientation of each fieldsource. From the specified locations and orientations, laws ofelectrodynamics determine the field values.

SUMMARY

There is provided in accordance with an embodiment of the presentdisclosure, a system including a catheter configured to be inserted intoa body-part of a living subject, and including an insertion tubeincluding a distal end, and a first coil-based position sensor disposedat the distal end, a pusher including a second coil-based positionsensor disposed thereon and a distal portion, and being configured to beadvanced and retracted through the insertion tube, and an expandableassembly including a plurality of flexible strips disposedcircumferentially around the distal portion of the pusher, with firstends of the strips connected to the distal end of the insertion tube andsecond ends of the strips connected to the distal portion of the pusher,the flexible strips being configured to bow radially outward when thepusher is retracted, at least one magnetic field radiator configured totransmit alternating magnetic fields into a region where the body-partis located, the first and second position sensors being configured tooutput respective first and second position signals in response to thetransmitted alternating magnetic fields, and processing circuitryconfigured to receive the first and second position signals from thefirst and second position sensors, compute location and orientationcoordinates for the first and second position sensors using a positioncomputation in which the location and orientation coordinates of each ofthe position sensors are interdependently computed in an iterativemanner responsively to the respective received position signals, andsubject to a constraint that the first and second position sensors arecoaxial, compute a distance between the computed location coordinates ofthe first position sensor and the computed location coordinates of thesecond position sensor, and estimate respective positions of theflexible strips responsively to at least the computed distance.

Further in accordance with an embodiment of the present disclosure, thesystem includes a display, wherein the processing circuitry isconfigured to compute a roll of the expandable assembly responsively tothe position signal from at least one of the first or second positionsensors, and render to the display a representation of at least a partof the catheter and the body-part responsively to the estimatedrespective positions of the flexible strips.

Still further in accordance with an embodiment of the present disclosurethe processing circuitry is configured to compute the location andorientation coordinates for one sensor of the first and second positionsensors using the position computation, and compute the locationcoordinates for another sensor of the first and second position sensorssubject to a constraint that the computed orientation coordinates forthe other sensor will be equal to the computed orientation coordinatesof the one sensor within a given tolerance.

Additionally, in accordance with an embodiment of the present disclosurethe processing circuitry is configured to compute initial location andinitial orientation coordinates for the first and second positionsensors using the position computation, compute an average of theinitial orientation coordinates of the first and second positionsensors, and compute the location and orientation coordinates for thefirst and second position sensors using the position computation subjectto a constraint that the orientation coordinates for the first andsecond position sensors will be equal to the computed average of theinitial orientation coordinates with a given tolerance.

Moreover, in accordance with an embodiment of the present disclosure theprocessing circuitry is configured to compute the location andorientation coordinates for the first and second position sensorssubject to a constraint that the computed orientation coordinates forthe first and second position sensors will be equal within a giventolerance.

There is also provided in accordance with another embodiment of thepresent disclosure, a system including a catheter configured to beinserted into a body-part of a living subject, and including aninsertion tube including a distal end, and a first coil-based positionsensor disposed at the distal end, a pusher including a secondcoil-based position sensor disposed thereon and a distal portion, andbeing configured to be advanced and retracted through the insertiontube, and an expandable assembly including a plurality of flexiblestrips disposed circumferentially around the distal portion of thepusher, with first ends of the strips connected to the distal end of theinsertion tube and second ends of the strips connected to the distalportion of the pusher, the flexible strips being configured to bowradially outward when the pusher is retracted, at least one magneticfield radiator configured to transmit alternating magnetic fields into aregion where the body-part is located, the first and second positionsensors being configured to output respective first and second positionsignals in response to the transmitted alternating magnetic fields, andprocessing circuitry configured to receive the first and second positionsignals from the first and second position sensors, compute a distanceand a relative orientation angle between the first and second positionsensors responsively to the received position signals, and estimaterespective positions of the flexible strips responsively to at least thecomputed distance and relative orientation angle, while accounting for adistortion of one or more of the flexible strips from a symmetricaldisposition when the relative orientation angle has a value greater thanzero.

Further in accordance with an embodiment of the present disclosure, thesystem includes a display, wherein the processing circuitry isconfigured to compute a roll of the expandable assembly responsively tothe position signal from at least one of the first or second positionsensors, and render to the display a representation of at least a partof the catheter and the body-part responsively to the estimatedrespective positions of the flexible strips.

There is also provided in accordance with still another embodiment ofthe present disclosure, a method, including inserting a catheter into abody-part of a living subject, the catheter including an insertion tube,a first coil-based position sensor disposed at a distal end of theinsertion tube, a pusher including a second coil-based position sensordisposed thereon, an expandable assembly including flexible stripsdisposed circumferentially around a distal portion of the pusher, withfirst ends of the strips connected to the distal end of the insertiontube and second ends of the strips connected to the distal portion ofthe pusher, retracting the pusher causing the flexible strips to bowradially outward, transmitting alternating magnetic fields into a regionwhere the body-part is located, outputting by the first and secondposition sensors respective first and second position signals inresponse to the transmitted alternating magnetic fields, receiving thefirst and second position signals from the first and second positionsensors, computing location and orientation coordinates for the firstand second position sensors using a position computation in which thelocation and orientation coordinates of each of the position sensors areinterdependently computed in an iterative manner responsively to therespective received position signals, and subject to a constraint thatthe first and second position sensors are coaxial, computing a distancebetween the computed location coordinates of the first position sensorand the computed location coordinates of the second position sensor, andestimating respective positions of the flexible strips responsively toat least the computed distance.

Still further in accordance with an embodiment of the presentdisclosure, the method includes computing a roll of the expandableassembly responsively to the position signal from at least one of thefirst or second position sensors, and rendering to a display arepresentation of at least a part of the catheter and the body-partresponsively to the estimated respective positions of the flexiblestrips.

Additionally, in accordance with an embodiment of the presentdisclosure, the method includes computing the location and orientationcoordinates for one sensor of the first and second position sensorsusing the position computation, and computing the location coordinatesfor another sensor of the first and second position sensors subject to aconstraint that the computed orientation coordinates for the othersensor will be equal to the computed orientation coordinates of the onesensor within a given tolerance.

Moreover, in accordance with an embodiment of the present disclosure,the method includes computing initial location and initial orientationcoordinates for the first and second position sensors using the positioncomputation, computing an average of the initial orientation coordinatesof the first and second position sensors, and computing the location andorientation coordinates for the first and second position sensors usingthe position computation subject to a constraint that the orientationcoordinates for the first and second position sensors will be equal tothe computed average of the initial orientation coordinates with a giventolerance.

Further in accordance with an embodiment of the present disclosure, themethod includes computing the location and orientation coordinates forthe first and second position sensors subject to a constraint that thecomputed orientation coordinates for the first and second positionsensors will be equal within a given tolerance.

There is also provided in accordance with still another embodiment ofthe present disclosure, a method, including inserting a catheter into abody-part of a living subject, the catheter including an insertion tube,a first coil-based position sensor disposed at a distal end of theinsertion tube, a pusher including a second coil-based position sensordisposed thereon, an expandable assembly including flexible stripsdisposed circumferentially around a distal portion of the pusher, withfirst ends of the strips connected to the distal end of the insertiontube and second ends of the strips connected to the distal portion ofthe pusher, retracting the pusher causing the flexible strips to bowradially outward, transmitting alternating magnetic fields into a regionwhere the body-part is located, outputting by the first and secondposition sensors respective first and second position signals inresponse to the transmitted alternating magnetic fields, receiving thefirst and second position signals from the first and second positionsensors, computing a distance and a relative orientation angle betweenthe first and second position sensors responsively to the receivedposition signals, and estimating respective positions of the flexiblestrips responsively to at least the computed distance and relativeorientation angle, while accounting for a distortion of one or more ofthe flexible strips from a symmetrical disposition when the relativeorientation angle has a value greater than zero.

Still further in accordance with an embodiment of the presentdisclosure, the method includes computing a roll of the expandableassembly responsively to the position signal from at least one of thefirst or second position sensors, and rendering to the display arepresentation of at least a part of the catheter and the body-partresponsively to the estimated respective positions of the flexiblestrips.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be understood from the following detaileddescription, taken in conjunction with the drawings in which:

FIG. 1 is a schematic, pictorial illustration of a system forelectro-anatomical mapping comprising a catheter, in accordance with anembodiment of the present invention;

FIG. 2A is a schematic view of a distal end of a basket catheter in acollapsed formation;

FIG. 2B is a schematic view of the distal end of the basket catheter ofFIG. 2A in a deployed formation;

FIG. 3A is a flowchart including steps in a method of operation of thesystem of FIG. 1 using the basket catheter of FIGS. 2A and B;

FIG. 3B is a flowchart including sub-steps in the method of operationFIG. 3A;

FIG. 3C is a flowchart including alternative sub-steps in the method ofoperation FIG. 3A;

FIG. 4A is a schematic view of a distal end of a basket catheter;

FIG. 4B is a schematic view of the distal end of the basket catheter ofFIG. 4A after being deformed to the side; and

FIG. 5 is a flowchart including steps in a method of operation of thesystem of FIG. 1 using the basket catheter of FIGS. 4A and B.

DESCRIPTION OF EXAMPLE EMBODIMENTS Overview

The Carto®3 system (produced by Biosense Webster, Inc., Irvine,California) applies Advanced Catheter Location (ACL) hybridposition-tracking technology. In ACL technology, distribution ofmeasured currents associated with probe electrodes on a catheter arecorrelated with a current-to-position matrix (CPM), which maps thecurrent distribution to a position of the catheter that was previouslyacquired from magnetic location-calibrated position signals. The ACLtechnology enables locating and visualizing a catheter (even a catheterwhich does not have a magnetic field sensor), but only in the volume(s)where the CPM has been computed, using a catheter with a magneticsensor. A prerequisite for building the CPM is to insert amagnetic-field sensor-equipped catheter into a body and move thecatheter in a volume of the body, in order to compute the CPM for thatvolume.

ACL technology may be used to track a basket catheter which haselectrodes on the basket. However, ACL technology, which measurescurrents or impedances, may not provide high enough accuracy in somesituations.

Embodiments of the present invention compute position coordinates of abasket catheter using magnetic-based tracking technology based on twocoil-based position sensors to provide an accurate computation of theposition of the basket and its electrodes. At least one magnetic fieldradiator transmits alternating magnetic fields into a region where abody-part is located and the coil-based position sensors outputrespective position signals in response to the transmitted alternatingmagnetic fields so that the respective position signals read from thecoils provide information about the position of the coils.

In some embodiments, the catheter includes an insertion tube including alumen and a first coil-based position sensor disposed at a distal end ofthe insertion tube. The catheter also includes a pusher including asecond coil-based position sensor disposed thereon. The pusher isadvanced and retracted through the lumen, as will be explained in moredetail below. The position sensors may be selected from single, dual, ortriple axis sensors, as will be described with reference to disclosedembodiments.

The catheter also includes an expandable assembly (e.g., basketassembly) comprising flexible strips disposed circumferentially aroundthe distal portion of the pusher, with first ends of the stripsconnected to the distal end of the insertion tube and second ends of thestrips connected to the distal end of the pusher. The flexible stripsbow radially outward when the pusher is retracted and flatten when thepusher is pushed in the direction of the distal end of the catheter.Each of the flexible strips includes multiple electrodes disposedthereon.

Although the strips are flexible, the strips are sturdy enough so that acomputed inter-coil distance between the first coil-based positionsensor and the second coil-based position sensor should provide anaccurate estimate of the shape of the flexible strips. However, thedifference between the inter-coil distance when the basket is fullydeployed and when the basket is fully closed may be around 4 mm for somebaskets and around 10 mm for other baskets, depending on the dimensionsof the basket. Additionally, the resolution of the magnetic-basedtracking technology may be around 1 mm Therefore, the inter-coildistance computed using the magnetic-based tracking technology may notbe accurate enough to accurately predict the shape of the flexiblestrips.

Some embodiments use a novel position computation to more accuratelycompute the inter-coil distance based on the assumption that the firstcoil-based position sensor and the second coil-based position sensor arecoaxial. In other words, one of the sensors includes a coil which iscoaxial with a coil of the other sensor and with the axis of theinsertion tube of the catheter. The novel position computation mayimprove the accuracy of position measurements from around 1 mm to around0.1 mm, by way of example only.

The system includes processing circuitry which receives the respectiveposition signals from the first and second position sensors. Theprocessing circuitry computes location and orientation coordinates forthe first and second position sensors using a position computation inwhich the location and orientation coordinates of each of the positionsensors are interdependently computed in an iterative mannerresponsively to the respective position signals. The positioncomputation is interdependent such that the location coordinatescomputed for one of the sensors based on the signal(s) received fromthat sensor is dependent upon the orientation coordinates computed forthat sensor, and vice-versa. Similarly, an error (e.g., due to noise orany other factor) in computing the location coordinates leads to aninaccuracy in computing orientation, and vice-versa.

Any suitable iterative position computation may be used. For example, USPatent Publication 2002/0198676 of Kirsch, et al., which is hereinincorporated by reference, describes an iterative position computationin its background section and some enhancements in the detaileddescription. The background section of Kirsch, et al., mentions thatdetermining a probes location and orientation from magnetic fieldmeasurements is not straight forward because the measured magneticfields are nonlinear functions of the location and orientation. Todetermine the probes location and orientation from the measured magneticfield values, the probes location and orientation are first presumed or“guessed” to be at a predicted location and orientation. An iterativeprocess is used to compare values of the magnetic field at the guessedprobe location and orientation with the measured field values. If themagnetic field values at a guessed location and orientation are close tothe measured values, the guessed location and orientation are presumedto accurately represent the actual location and orientation of theprobe. The position computations described in the Kirsch, et al.,publication may provide suitable iterative position computations,mutatis mutandis, for use in embodiments of the present disclosure. Forexample, the iterative position computations described in Kirsch, etal., may be subject to a constraint with respect to the orientation asdescribed below.

European Patent Publication 1,126,787 of Golden, et al., which is hereinincorporated by reference, describes an iterative position computationwhich may provide a suitable iterative position computation, mutatismutandis, for use in embodiments of the present disclosure.

Based on the interdependent and iterative nature of the computation,improvement in accuracy of location measurements may be achieved bysubjecting the position computation to a constraint that the first andsecond position sensors are coaxial based on the known geometry of thecatheter and therefore both sensors have a same orientation which isused in the position computation of both sensors.

In some embodiments, the processing circuitry computes the location andorientation coordinates for the first and second position sensorssubject to a constraint that the computed orientation coordinates forthe first and second position sensors will be equal to within a giventolerance. Forcing the orientation coordinates to be equal generallyresults in more accurately computed location coordinates.

In other embodiments, the processing circuitry computes the location andorientation coordinates for one of the sensors (sensor A) using theposition computation and then computes the location coordinates for theother sensor (sensor B) subject to a constraint that the computedorientation coordinates for sensor B will be equal to the alreadycomputed orientation coordinates of sensor A to within a giventolerance, such as plus or minus 2 degrees.

In yet other embodiments, the processing circuitry computes initiallocation and initial orientation coordinates for both sensors using theposition computation based on the signals received from the sensors andthen computes an average of the initial orientation coordinates of bothsensors. The processing circuitry then computes the location andorientation coordinates for each sensor using the position computationbased on the signals received from the respective sensors and subject toa constraint that the final computed orientation coordinates for eachsensor will be equal to the computed average of the initial orientationcoordinates to within a given tolerance, such as plus or minus 2degrees.

The computed location coordinates of the first and second sensor may beused to compute a distance between the first and second position sensor.

Based on a knowledge of the mechanical properties of the flexible stripsand/or by performing pre-calibration to find which inter-coil distancescorrespond to which bowing of the flexible strips (at various distancebetween the sensors), respective positions of the flexible strips may beestimated responsively to computed distance as well as a roll of thebasket which may be computed from signals of a dual-axis or triple-axisposition sensor disposed on the catheter. The processing circuitryrenders to a display a representation of at least a part of the catheterand the body-part responsively to the estimated respective positions ofthe flexible strips and the computed roll.

In some embodiments, improved distance measurements may be provided byone of the sensors being used as a local transmitter, and the othersensor as a local receiver. The transmitter may then transmit signals tothe receiver in a different frequency than is used by the magnetic fieldradiator(s) described above. The locally transmitted and receivedsignals may provide additional information regarding the locations ofboth sensors (such as the distance between the sensors according to theintensity of the received signal) and this may be used to increase theaccuracy of the basket visualization.

In some embodiments, where the pusher and basket are flexible enough tobe push to one side (for example, when pressed against tissue in thebody-part) with respect to an axis of the insertion tube, the processingcircuitry may compute a distance and a relative orientation anglebetween the first and second position sensors responsively to thereceived position signals. A non-zero relative orientation angle is thenindicative that the expandable assembly (e.g., the basket) is deflectedto a side with respect to an axis of the insertion tube, and that atleast some of the flexible strips are distorted as compared to a shapeof the flexible strips when the expandable assembly is centrallypositioned around the axis of the insertion tube. Based on a knowledgeof the mechanical properties of the flexible strips and/or by performingpre-calibration to find which relative orientation angle corresponds towhich deformation of the flexible strips (at distance between thesensors), respective positions of the flexible strips (including thedistorted flexible strips) may be estimated responsively to at least thecomputed distance and relative orientation angle while accounting for adistortion of one or more of the flexible strips from a symmetricaldisposition when the relative orientation angle has a value greater thanzero.

System Description

Documents incorporated by reference herein are to be considered anintegral part of the application except that, to the extent that anyterms are defined in these incorporated documents in a manner thatconflicts with definitions made explicitly or implicitly in the presentspecification, only the definitions in the present specification shouldbe considered. As used herein, the terms “about” or “approximately” forany numerical values or ranges indicate a suitable dimensional tolerancethat allows the part or collection of components to function for itsintended purpose as described herein. More specifically, “about” or“approximately” may refer to the range of values ±20% of the recitedvalue, e.g. “about 90%” may refer to the range of values from 71% to99%.

Reference is now made to FIG. 1 , which is a schematic, pictorialillustration of a catheter tracking system 20, in accordance with anembodiment of the present invention. The system 20 includes a catheter40 configured to be inserted into a body part of a living subject (e.g.,a patient 28). A physician 30 navigates the catheter 40 (for example, abasket catheter produced Biosense Webster, Inc. of Irvine, CA, USA),seen in detail in inset 45, to a target location in a heart 26 of thepatient 28, by manipulating a deflectable segment of an insertion tube22 of the catheter 40, using a manipulator 32 near a proximal end 29 ofthe insertion tube 22, and/or deflection from a sheath 23. In thepictured embodiment, physician 30 uses catheter 40 to performelectro-anatomical mapping of a cardiac chamber.

The insertion tube 22 includes a distal end 33 The catheter 40 includesan assembly 35 (e.g., a basket assembly) on which multiple electrodes 48(only some labeled for the sake of simplicity) are disposed. Theassembly 35 is disposed distally to the insertion tube 22 and may beconnected to the insertion tube 22 via a coupling member of theinsertion tube 22 at the distal end 33. The coupling member of theinsertion tube 22 may formed as an integral part of the rest of theinsertion tube 22 or as a separate element which connects with the restof the insertion tube 22.

The assembly 35 further comprises multiple flexible strips 55 (only onelabeled for the sake of simplicity), to each of which are coupled theelectrodes 48. The assembly 35 may include any suitable number ofelectrodes 48. In some embodiments, the assembly 35 may include tenflexible strips 55 and 120 electrodes, with 12 electrodes disposed oneach flexible strip 55.

The catheter 40 includes a pusher 37. The pusher 37 is typically a tubethat is disposed in a lumen of the insertion tube 22 and spans from theproximal end 29 to the distal end 33 of the insertion tube 22. A distalend of the pusher 37 is connected to first ends of the flexible strips55, typically via a coupling member of the pusher 37. The couplingmember of the pusher 37 may formed as an integral part of the rest ofthe pusher 37 or as a separate element which connects with the rest ofthe pusher 37. The distal end of the insertion tube 22 is connected tosecond ends of the flexible strips 55, typically via the coupling memberof the distal end 33. The pusher 37 is generally controlled via themanipulator 32 to deploy the assembly 35 and change an ellipticity ofthe assembly 35 according to the longitudinal displacement of the pusher37 with respect to the insertion tube 22.

The actual basket assembly 35 structure may vary. For example, flexiblestrips 55 may be made of a printed circuit board (PCB), or of ashape-memory alloy.

Embodiments described herein refer mainly to a basket distal-endassembly 35, purely by way of example. In alternative embodiments, thedisclosed techniques can be used with a catheter having a balloon-baseddistal-end assembly or of any other suitable type of distal-endassembly.

Catheter 40 is inserted in a folded configuration, through sheath 23,and only after the catheter 40 exits sheath 23 does catheter 40 regainits intended functional shape. By containing catheter 40 in a foldedconfiguration, sheath 23 also serves to minimize vascular trauma on itsway to the target location.

Catheter 40 may incorporate a magnetic sensor 50A, seen in inset 45, atthe distal edge of insertion tube 22 (i.e., at the proximal edge ofbasket assembly 35). Typically, although not necessarily, sensor 50A isa Single-Axis Sensor (SAS). A second magnetic sensor 50B may be includedat any suitable position on the pusher 37. Sensor 50B may be aTriple-Axis Sensor (TAS) or a Dual-Axis Sensor (DAS), or a SAS by way ofexample only, based for example on sizing considerations.

Magnetic sensors 50A and 50B and electrodes 48 are connected by wiresrunning through insertion tube 22 to various driver circuitries in aconsole 24.

In some embodiments, system 20 comprises a magnetic-sensing sub-systemto estimate an ellipticity of the basket assembly 35 of catheter 40, aswell as its elongation/retraction state, inside a cardiac chamber ofheart 26 by estimating the elongation of the basket assembly 35 from thedistance between sensors 50A and 50B. Patient 28 is placed in a magneticfield generated by a pad containing one or more magnetic field generatorcoils 42, which are driven by a unit 43. The magnetic fields generatedby coil(s) 42 transmit alternating magnetic fields into a region wherethe body-part is located. The transmitted alternating magnetic fieldsgenerate signals in sensors 50A and 50B, which are indicative ofposition and/or direction. The generated signals are transmitted toconsole 24 and become corresponding electrical inputs to processingcircuitry 41. The processing circuitry 41 uses the signals to calculatethe elongation of the basket assembly 35, and to estimate basketellipticity and elongation/retraction state from the calculated distancebetween sensors 50A and 50B, described in more detail below withreference to FIGS. 2-5 .

The method of position and/or direction sensing using external magneticfields and magnetic sensors, such as 50A and 50B, is implemented invarious medical applications, for example, in the CARTO® system,produced by Biosense-Webster, and is described in detail in U.S. Pat.Nos. 5,391,199, 6,690,963, 6,484,118, 6,239,724, 6,618,612 and6,332,089, in PCT Patent Publication WO 96/05768, and in U.S. PatentApplication Publications 2002/0065455 A1, 2003/0120150 A1 and2004/0068178 A1, whose disclosures are all incorporated herein byreference.

Processing circuitry 41, typically part of a general-purpose computer,is further connected via a suitable front end and interface circuits 44,to receive signals from surface-electrodes 49. Processing circuitry 41is connected to surface-electrodes 49 by wires running through a cable39 to the chest of patient 28.

The catheter 40 includes a connector 47 disposed at the proximal end 29of the insertion tube 22 for coupling to the processing circuitry 41.

In an embodiment, processing circuitry 41 renders to a display 27, arepresentation 31 of at least a part of the catheter 40 and a body-part,from a scan (e.g., CT or MRI) of the body-part previously registeredwith the system 20, responsively to computed position coordinates of theinsertion tube 22 and the flexible strips 55, described in more detailwith reference to FIGS. 2-5 .

Processing circuitry 41 is typically programmed in software in a generalpurpose microprocessor to transform the general purpose microprocessorinto a specific processor and carry out the functions described herein.The software may be downloaded to the computer in electronic form, overa network, for example, or it may, alternatively or additionally, beprovided and/or stored on non-transitory tangible media, such asmagnetic, optical, or electronic memory.

The example illustration shown in FIG. 1 is chosen purely for the sakeof conceptual clarity. FIG. 1 shows only elements related to thedisclosed techniques for the sake of simplicity and clarity. System 20typically comprises additional modules and elements that are notdirectly related to the disclosed techniques, and thus are intentionallyomitted from FIG. 1 and from the corresponding description. The elementsof system 20 and the methods described herein may be further applied,for example, to control an ablation of tissue of heart 26.

Reference is now made to FIGS. 2A and 2B. FIG. 2A is a schematic view ofa distal end of the basket catheter 40 in a collapsed formation. FIG. 2Bis a schematic view of the distal end of the basket catheter 40 of FIG.2A in a deployed formation.

The magnetic sensor 50A is a coil-based position sensor disposed at thedistal end 33 of the insertion tube 22, for example, in the couplingmember at the distal end 33. The magnetic sensor 50B is a coil-basedposition sensor disposed on a distal portion 52 of the pusher 37, forexample, in a coupling member of the distal portion 52, coupling thedistal ends of the flexible strips 55 to pusher 37. The pusher 37 isconfigured to be advanced and retracted through the insertion tube 22.Each sensor 50A, 50B may be a SAS, DAS or TAS. The sensors 50A, 50B maybe the same type of sensor, or different types of sensor. If both of thesensors 50A, 50B are single-axis sensors, the catheter 40 generallyincludes another position sensor to track a roll of the assembly 35. Themagnetic sensors 50A, 50B are configured to output respective first andsecond position signals in response to the transmitted alternatingmagnetic fields transmitted by the magnetic field generator coil(s) 42(FIG. 1 ).

The assembly 35 is typically an expandable assembly comprising theflexible strips 55 (only some labeled for the sake of simplicity)disposed circumferentially around the distal portion 52 of the pusher 37with first ends of the strips 55 connected to the distal end 33 (e.g.,the coupling member of the distal end 33) of the insertion tube 22 andsecond ends of the strips 55 connected to the distal portion 52 (e.g.,the coupling member of the distal portion 52) of the pusher 37. Theflexible strips 55 are configured to bow radially outward when thepusher 37 is retracted. A plurality of the electrodes 48 (only somelabeled for the sake of simplicity) are disposed on each of the flexiblestrips 55.

Reference is now made to FIG. 3A, which is a flowchart 60 includingsteps in a method of operation of the system 20 of FIG. 1 using thebasket catheter 40 of FIGS. 2A and B.

The processing circuitry 41 (FIG. 1 ) is configured to receive (block62) the first and second position signals from the magnetic sensors 50A,50B, respectively. In some embodiments, the magnetic sensor 50A mayprovide one or more position signals corresponding to one or more coilsof the magnetic sensor 50A. Similarly, the magnetic sensor 50B mayprovide one or more position signals corresponding to one or more coilsof the magnetic sensor 50B.

The processing circuitry 41 is configured to compute (block 64) locationand orientation coordinates for the magnetic sensors 50A, 50B based onthe received signals, and using a position computation in which thelocation and orientation coordinates of each of the magnetic sensors50A, 50B are interdependently computed in an iterative mannerresponsively to the respective received position signal, and subject toa constraint that the magnetic sensors 50A, 50B (include coils that) arecoaxial and therefore have a same orientation.

In some embodiments, the processing circuitry 41 is configured tocompute the location and orientation coordinates for the magneticsensors 50A, 50B subject to a constraint that the computed orientationcoordinates for the magnetic sensors 50A, 50B will be equal within agiven tolerance, such as plus or minus 2 degrees. The step of block 64is described in more detail with reference to FIGS. 3B and 3C.

The processing circuitry 41 is configured to compute (block 66) adistance between the computed location coordinates of the magneticsensor 50A and the computed location coordinates of the magnetic sensor50B. The computed distance is indicative of the bow of the flexiblestrips 55 (FIG. 2B) and the general shape of the basket assembly 35(FIG. 2B) as will be described below in more detail with reference tothe step of block 70.

The processing circuitry 41 is configured to compute (block 68) a rollof the expandable assembly 35 responsively to the position signal(s)from the magnetic sensor 50A and/or from the magnetic sensor 50B and/orfrom another position sensor of the catheter 40. As mentionedpreviously, the sensor providing data for computation of roll istypically a DAS or TAS.

The bow of the flexible strips 55 and/or the positions of the electrodes48 (or other features) on the flexible strips 55 with respect to a fixedpoint on the catheter 40 (such as the distal tip of the insertion tube22) may be measured for various distances between the magnetic sensors50A, 50B. For example, the positions of the electrodes 48 with respectto a fixed point on the catheter 40 may be measured for every 0.2 mmmovement of the pusher 37 with respect to the insertion tube 22, andafter each 0.2 mm movement, the computed distance between the magneticsensors 50 is recorded along with the positions of the electrodes 48.This data may then be used to find the bow of the flexible strips 55and/or the positions of the electrodes 48 (or other features) on theflexible strips 55 with respect to a fixed point on the catheter 40(such as the distal tip of the insertion tube 22) responsively to thecomputed distance between the magnetic sensors 50.

In some embodiments, the bow of the flexible strips 55 and/or thepositions of the electrodes 48 (or other features) on the flexiblestrips 55 with respect to a fixed point on the catheter 40 (such as thedistal tip of the insertion tube 22) may be computed based on thecomputed distance between the magnetic sensors 50 and a model of thecatheter 40 which provides the bow of the flexible strips 55 and/or thepositions of the electrodes 48 for the computed distance based on themechanical properties and dimensions of the flexible strips 55.

The processing circuitry 41 is configured to estimate (block 70)respective positions of the flexible strips 55 responsively to thecomputed distance, the computed roll and the computed location andorientation coordinates of one or more of the magnetic sensors 50. Thecomputed distance provides the respective positions of the flexiblestrips 55 with respect to a fixed point of the catheter 40. The computedroll, location and orientation coordinates of one or more of themagnetic sensors 50 provides the respective positions of the flexiblestrips 55 with respect to a magnetic coordinate frame used in the system20.

The processing circuitry 41 is configured to render (block 72) to thedisplay 27 (FIG. 1 ), the representation 31 (FIG. 1 ) of at least a partof the catheter 40 and the body-part (e.g., the heart 26) responsivelyto the estimated respective positions of the flexible strips 55 and acomputed position of the insertion tube 22 (for example, based onsignal(s) received from the magnetic sensor 50A).

Reference is now made to FIG. 3B, which is a flowchart 74 includingsub-steps in the method of operation FIG. 3A. The following sub-stepsare sub-steps of the step of block 64 of FIG. 3A.

The processing circuitry 41 (FIG. 1 ) is configured to compute (block76) the location and orientation coordinates for one sensor of themagnetic sensors 50A, 50B using the position computation, responsivelyto the received signal(s) of the one sensor. The processing circuitry 41is configured to compute (block 78) the location coordinates for theother sensor of the magnetic sensors 50A, 50B using the positioncomputation, subject to a constraint that the computed orientationcoordinates for the other sensor will be equal to the computedorientation coordinates of the one sensor within a given tolerance, suchas plus or minus 2 degrees.

Reference is now made to FIG. 3C, which is a flowchart 80 includingalternative sub-steps in the method of operation FIG. 3A. The followingsub-steps are sub-steps of the step of block 64 of FIG. 3A.

The processing circuitry 41 (FIG. 1 ) is configured to compute (block82) initial location and initial orientation coordinates for both themagnetic sensors 50 using the position computation.

The processing circuitry 41 is configured to compute (block 84) anaverage of the initial orientation coordinates of the magnetic sensors50. For example, if the orientation coordinates are represented by twoangles θ, φ, for example representing yaw and pitch respectively, theorientation of magnetic sensor 50A being θ_(A), φ_(A) and theorientation of magnetic sensor 50B being θ_(B), φ_(B), the averageorientation of the magnetic sensor 50 is equal to the θ_(av), φ_(av),where θ_(av) is the average of θ_(A) and θ_(B), and φ_(av) is theaverage of φ_(A) and φ_(B).

The processing circuitry 41 is configured to compute (block 86) thelocation and orientation coordinates for magnetic sensors 50 using theposition computation based on the signals received from the sensors 50and subject to a constraint that the orientation coordinates for bothmagnetic sensors 50 will be equal to the computed average of the initialorientation coordinates within a given tolerance, such as plus or minus2 degrees.

Reference is now made to FIGS. 4A and 4B. FIG. 4A is a schematic view ofa distal end of a basket catheter 90. FIG. 4B is a schematic view of thedistal end of the basket catheter 90 of FIG. 4A after being deformed tothe side. The basket catheter 90 is substantially the same as thecatheter 40 of FIGS. 2A and 2B except that basket catheter 90 includes apusher 92 and an expandable assembly 94 (e.g., basket) that can bepushed to the side with respect to the axis of an insertion tube 96 ofthe basket catheter 90. For example, when the expandable assembly 94 ispushed against tissue, the expandable assembly 94 may deform. Similarly,to the catheter 40 of FIG. 2A, the basket catheter 90 includes multipleflexible strips 98 (only some labeled for the sake of simplicity),electrodes 100 (only some labeled for the sake of simplicity) disposedon each of the flexible strips 98, and two magnetic sensors 102A, 102B(similar to the magnetic sensors 50 of FIG. 2A). The magnetic sensor102A is disposed at the distal end of the insertion tube 96 (e.g., in acoupling member coupling the insertion tube 96 to the assembly 94) andthe magnetic sensor 102B is disposed at the distal end of the pusher 92(e.g., in a coupling member coupling the pusher 92 with distal ends ofthe flexible strips 98).

FIG. 4B shows that some of the flexible strips 98 are more bowed thanothers due to the expandable assembly 94 being pushed against tissue.For example, the flexible strip 98-1 is more bowed than the otherflexible strips 98. Additionally, some of the flexible strips 98, e.g.,the flexible strip 98-2, are less bowed than they would be if theexpandable assembly 94 was not pushed against tissue. It can also beclearly seen from FIG. 4B that the magnetic sensors 102 are not coaxialand that the axis of the magnetic sensor 102B is pointing away from theaxis of the insertion tube 96 that includes the magnetic sensor 102A.

Reference is now made to FIG. 5 , which is a flowchart 110 includingsteps in a method of operation of the system 20 of FIG. 1 using thebasket catheter 90 of FIGS. 4A and B. Reference is also made to FIGS. 4Aand 4B.

The processing circuitry 41 (FIG. 1 ) is configured to receive (block112) first and second position signals from the magnetic sensors 102A,102B, respectively. In some embodiments, the magnetic sensor 102A mayprovide one or more position signals corresponding to one or more coilsof the magnetic sensor 102A. Similarly, the magnetic sensor 102B mayprovide one or more position signals corresponding to one or more coilsof the magnetic sensor 102B.

The processing circuitry 41 is configured to compute (block 114) adistance and a relative orientation angle between the magnetic sensors102 responsively to the received position signals. The relativeorientation angle having a value greater than zero is generallyindicative that the expandable assembly 94 is deflected to a side withrespect to an axis of the insertion tube 96, and that at least some ofthe flexible strips 98 are distorted as compared to a shape of theflexible strips 98 when the expandable assembly 94 is centrallypositioned around the axis of the insertion tube 96.

The processing circuitry 41 is configured to compute (block 116) a rollof the expandable assembly 94 responsively to the position signal(s)from one or more of the magnetic sensors 102 or from another sensordisposed on the basket catheter 90.

The bow of the flexible strips 98 and/or the positions of the electrodes100 (or other features) on the flexible strips 98 with respect to afixed point on the catheter 90 (such as the distal tip of the insertiontube 96) may be measured for various distances between the magneticsensors 102 and for various relative orientation angles between themagnetic sensors 102. For example, the positions of the electrodes 100with respect to the fixed point on the catheter 90 may be measured forapproximately every 0.2 mm movement of the pusher 92 with respect to theinsertion tube 96 and for every 1 degree of relative orientation betweenthe magnetic sensors 102 (up to a maximum sideways movement of theexpandable assembly 94). At each different distance/relative-orientationcombination, the computed distance and computed relative orientationangle between the magnetic sensors 50 is recorded along with theposition data of the electrodes 100. This data may then be used toestimate the bow of the flexible strips 98 and/or the positions of theelectrodes 100 (or other features) on the flexible strips 100 withrespect to a fixed point on the catheter 90 (such as the distal tip ofthe insertion tube 96) responsively to the computed distance andrelative orientation angle between the magnetic sensors 102.

Additionally, or alternatively, the bow of the flexible strips 98 may beestimated based on the following assumptions: (a) each of the flexiblestrips 98 is of a fixed and known length; (b) each of the flexiblestrips 98 is connected to the coupling member, which couples the pusher92 with the distal ends of the flexible strips 98, substantiallyperpendicular (within an error of plus or minus 10 degrees) to alongitudinal axis of that coupling member; (c) each of the flexiblestrips 98 is connected to the coupling member, which couples theproximal ends of the flexible strips 98 to the insertion tube 96,substantially parallel (within an error of plus or minus 10 degrees) tothe longitudinal axis of the insertion tube 96. Based on the aboveassumptions (a)-(c), and the computed positions of the coupling membersbased on the computed positions of the magnetic sensors 102, the bow ofeach of the flexible strips 98 may be computed using a third-degreepolynomial. In some embodiments, the bow of the flexible strips 98and/or the positions of the electrodes 100 (or other features) on theflexible strips 98 with respect to a fixed point on the catheter 90(such as the distal tip of the insertion tube 96) may be computed basedon the computed distance and orientation between the magnetic sensors102 and a model of the catheter 90 which provides the bow of theflexible strips 98 and/or the positions of the electrodes 100 for thecomputed distance based on the mechanical properties and dimensions ofthe flexible strips 98.

The processing circuitry 41 is configured to estimate (block 118)respective positions of the flexible strips 98 responsively to at leastthe computed distance and relative orientation angle, while accountingfor a distortion of one or more of the flexible strips 98 from asymmetrical disposition when the relative orientation angle has a valuegreater than zero. The computed distance and relative orientation anglebetween the magnetic sensors 102 provide the respective positions of theflexible strips 98 with respect to a fixed point of the catheter 90. Thecomputed roll, location and orientation coordinates of one or more ofthe magnetic sensors 102 provides the respective positions of theflexible strips 98 with respect to the magnetic coordinate frame used inthe system 20.

The processing circuitry 41 is configured to render (block 120) to thedisplay 27 (FIG. 1 ), the representation 31 (FIG. 1 ) of at least a partof the catheter 90 and the body-part (e.g., the heart 26) responsivelyto the estimated respective positions of the flexible strips 98 and acomputed position of the insertion tube 96 (for example, based onsignal(s) received from the magnetic sensor 102A).

Various features of the invention which are, for clarity, described inthe contexts of separate embodiments may also be provided in combinationin a single embodiment. Conversely, various features of the inventionwhich are, for brevity, described in the context of a single embodimentmay also be provided separately or in any suitable sub-combination.

The embodiments described above are cited by way of example, and thepresent invention is not limited by what has been particularly shown anddescribed hereinabove. Rather the scope of the invention includes bothcombinations and subcombinations of the various features describedhereinabove, as well as variations and modifications thereof which wouldoccur to persons skilled in the art upon reading the foregoingdescription and which are not disclosed in the prior art.

What is claimed is:
 1. A system comprising: a catheter configured to beinserted into a body-part of a living subject, and comprising: aninsertion tube including a distal end, and a first coil-based positionsensor disposed at the distal end; a pusher including a secondcoil-based position sensor disposed thereon and a distal portion, andbeing configured to be advanced and retracted through the insertiontube; and an expandable assembly comprising a plurality of flexiblestrips disposed circumferentially around the distal portion of thepusher, with first ends of the flexible strips connected to the distalend of the insertion tube and second ends of the flexible stripsconnected to the distal portion of the pusher, the flexible strips beingconfigured to bow radially outward when the pusher is retracted; atleast one magnetic field radiator configured to transmit alternatingmagnetic fields into a region where the body-part is located, the firstand second coil-based position sensors being configured to outputrespective first and second position signals in response to thetransmitted alternating magnetic fields; and processing circuitryconfigured to: receive the first and second position signals from thefirst and second coil-based position sensors; compute a distance and arelative orientation angle between the first and second coil-basedposition sensors responsively to the received position signals; andestimate respective positions of the flexible strips responsively to atleast the computed distance and relative orientation angle, whileaccounting for a distortion of one or more of the flexible strips from asymmetrical disposition when the relative orientation angle has a valuegreater than zero.
 2. The system according to claim 1, wherein theprocessing circuitry is configured to compute a roll of the expandableassembly responsively to the position signal from at least one of thefirst or second coil-based position sensors.
 3. The system according toclaim 2, further comprising a display, wherein the processing circuitryis configured to render to the display a representation of at least apart of the catheter and the body-part responsively to the estimatedrespective positions of the flexible strips.
 4. The system according toclaim 1, wherein the processing circuitry is configured to: compute thelocation and orientation coordinates for one sensor of the first andsecond coil-based position sensors using the position computation; andcompute the location coordinates for another sensor of the first andsecond coil-based position sensors subject to a constraint that thecomputed orientation coordinates for the other sensor will be equal tothe computed orientation coordinates of the one sensor within a giventolerance.
 5. The system according to claim 4, wherein the giventolerance is approximately plus or minus two degrees.
 6. The systemaccording to claim 1, wherein the processing circuitry is configured to:compute initial location and initial orientation coordinates for thefirst and second coil-based position sensors using the positioncomputation; compute an average of the initial orientation coordinatesof the first and second coil-based position sensors; and compute thelocation and orientation coordinates for the first and second coil-basedposition sensors using the position computation subject to a constraintthat the orientation coordinates for the first and second coil-basedposition sensors will be equal to the computed average of the initialorientation coordinates with a given tolerance.
 7. The system accordingto claim 1, wherein the processing circuitry is configured to computethe location and orientation coordinates for the first and secondcoil-based position sensors subject to a constraint that the computedorientation coordinates for the first and second coil-based positionsensors will be equal within a given tolerance.
 8. The system accordingto claim 1, wherein at least one of the first and second coil-basedposition sensors comprises a dual-axis position sensor.
 9. The systemaccording to claim 1, wherein at least one of the first coil-basedposition sensor comprises a triple-axis position sensor.
 10. The systemaccording to claim 1, wherein the first and second coil-based positionsensors are coaxial.
 11. The system according to claim 1, wherein theplurality of flexible strips comprises a plurality of electrodes. 12.The system according to claim 11, wherein at least some of theelectrodes of the plurality of electrodes are configured to detectelectrophysiological signals for electro-anatomical mapping.
 13. Thesystem according to claim 11, wherein at least some of the electrodes ofthe plurality of electrodes are configured to deliver ablative energy totissue.
 14. A method, comprising: inserting a catheter into a body-partof a living subject, the catheter comprising an insertion tube, a firstcoil-based position sensor disposed at a distal end of the insertiontube, a pusher including a second coil-based position sensor disposedthereon, an expandable assembly including flexible strips disposedcircumferentially around a distal portion of the pusher, with first endsof the strips connected to the distal end of the insertion tube andsecond ends of the strips connected to the distal portion of the pusher;retracting the pusher causing the flexible strips to bow radiallyoutward; transmitting alternating magnetic fields into a region wherethe body-part is located; outputting by the first and second coil-basedposition sensors respective first and second position signals inresponse to the transmitted alternating magnetic fields; receiving thefirst and second position signals from the first and second coil basedposition sensors; computing a distance and a relative orientation anglebetween the first and second coil-based position sensors responsively tothe received position signals; and estimating respective positions ofthe flexible strips responsively to at least the computed distance andrelative orientation angle, while accounting for a distortion of one ormore of the flexible strips from a symmetrical disposition when therelative orientation angle has a value greater than zero.
 15. The methodaccording to claim 14, further comprising: computing a roll of theexpandable assembly responsively to the position signal from at leastone of the first or second coil-based position sensors; and rendering toa display a representation of at least a part of the catheter and thebody-part responsively to the estimated respective positions of theflexible strips.
 16. The method according to claim 14, furthercomprising: computing the location and orientation coordinates for onesensor of the first and second coil-based position sensors using theposition computation; and computing the location coordinates for anothersensor of the first and second coil-based position sensors subject to aconstraint that the computed orientation coordinates for the othersensor will be equal to the computed orientation coordinates of the onesensor within a given tolerance.
 17. The method according to claim 14,further comprising: computing initial location and initial orientationcoordinates for the first and second coil-based position sensors usingthe position computation; computing an average of the initialorientation coordinates of the first and second coil-based positionsensors; and computing the location and orientation coordinates for thefirst and second coil-based position sensors using the positioncomputation subject to a constraint that the orientation coordinates forthe first and second coil-based position sensors will be equal to thecomputed average of the initial orientation coordinates with a giventolerance.
 18. The method according to claim 14, further comprisingcomputing the location and orientation coordinates for the first andsecond coil-based position sensors subject to a constraint that thecomputed orientation coordinates for the first and second coil-basedposition sensors will be equal within a given tolerance.
 19. The methodaccording to claim 14, wherein the first and second coil-based positionsensors are coaxial.
 20. The method according to claim 14, wherein theplurality of flexible strips comprises a plurality of electrodes.